Pharmacokinetic modeling of ascorbate diffusion through normal and tumor tissue

Free Radical Biology and Medicine 77 (2014) 340–352

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Original Contribution

Pharmacokinetic modeling of ascorbate diffusion through normal and tumor tissue Caroline Kuiper a,n,1, Margreet C.M. Vissers a, Kevin O. Hicks b a b

Centre for Free Radical Research, Pathology Department, University of Otago at Christchurch, Christchurch, New Zealand Auckland Cancer Society Research Centre, University of Auckland, Auckland, New Zealand

art ic l e i nf o

a b s t r a c t

Article history: Received 28 July 2014 Received in revised form 12 September 2014 Accepted 19 September 2014 Available online 30 September 2014

Ascorbate is delivered to cells via the vasculature, but its ability to penetrate into tissues remote from blood vessels is unknown. This is particularly relevant to solid tumors, which often contain regions with dysfunctional vasculature, with impaired oxygen and nutrient delivery, resulting in upregulation of the hypoxic response and also the likely depletion of essential plasma-derived biomolecules, such as ascorbate. In this study, we have utilized a well-established multicell-layered, three-dimensional pharmacokinetic model to measure ascorbate diffusion and transport parameters through dense tissue in vitro. Ascorbate was found to penetrate the tissue at a slightly lower rate than mannitol and to travel via the paracellular route. Uptake parameters into the cells were also determined. These data were fitted to the diffusion model, and simulations of ascorbate pharmacokinetics in normal tissue and in hypoxic tumor tissue were performed with varying input concentrations, ranging from normal dietary plasma levels (10–100 μM) to pharmacological levels ( 41 mM) as seen with intravenous infusion. The data and simulations demonstrate heterogeneous distribution of ascorbate in tumor tissue at physiological blood levels and provide insight into the range of plasma ascorbate concentrations and exposure times needed to saturate all regions of a tumor. The predictions suggest that supraphysiological plasma ascorbate concentrations ( 4100 μM) are required to achieve effective delivery of ascorbate to poorly vascularized tumor tissue. & 2014 Elsevier Inc. All rights reserved.

Keywords: Ascorbate Tumor hypoxia Pharmacokinetics Hypoxia-inducible factor-1 2-Oxoglutarate-dependent dioxygenases Free radicals

Introduction Ascorbate (vitamin C) circulates through the vasculature and is actively taken up into tissue cells via the sodium-dependent vitamin C transporters (SVCTs)2 [1]. The effective intracellular concentration varies significantly with plasma levels, but little is known of the ability of ascorbate to penetrate into the tissues and reach cells more remote from the vasculature. This is of interest in determining the effective dose of dietary ascorbate required for tissue saturation and, in particular, for those tissues with a poor blood supply. The latter scenario is particularly relevant to solid tumors that are known to contain regions of poor perfusion and hypoxia [2], caused by high intervessel distances that exceed the diffusion distance of oxygen [3], as well as poorly functional and

Abbreviations used: 2-OGDD, 2-oxoglutarate-dependent dioxygenase; HIF-1, hypoxia-inducible factor-1; 3D, three-dimensional; MCL, multicellular layer; SVCT, sodium-dependent vitamin C transporter n Corresponding author. E-mail address: [email protected] (C. Kuiper). 1 Current address: Centre for Cellular and Molecular Physiology, Nuffield Department of Medicine, University of Oxford, Old Road Campus, Oxford OX3 7BN, UK. http://dx.doi.org/10.1016/j.freeradbiomed.2014.09.023 0891-5849/& 2014 Elsevier Inc. All rights reserved.

leaky vessels causing temporary oxygen fluctuations [4]. In addition to a lack of oxygen, we hypothesize that these regions may lack other essential biomolecules delivered by the vasculature, such as ascorbate. Plasma ascorbate levels are tightly controlled and do not normally exceed
100 μM with dietary intake [5]. The SVCT1 tightly regulates the plasma concentration, as it has saturable transport kinetics at both the intestine and the kidney to limit absorption and reabsorption [6]. More recently, there has been increasing interest in the intravenous administration of ascorbate, which bypasses this tight control and can yield plasma levels up to 300-fold higher, with maximum levels of up to 30 mM, albeit transiently [7]. Whether these high concentrations would significantly increase delivery to inaccessible tumor tissue or affect cellular uptake is unknown. A major function for ascorbate in vivo is as an essential cofactor for the 2-oxoglutarate-dependent dioxygenases (2-OGDDs). The 2-OGDDs require 2-oxoglutarate, molecular oxygen, ferrous iron, and ascorbate for activity and can therefore act as metabolic sensors, relaying a drop in the level of these metabolites to changes in gene expression and cellular function [8,9]. These enzymes perform hydroxylation reactions on various substrates including RNA, DNA, histones, ribosomes, prohormones, and proteins [10]. Accordingly, most cells and tissues accumulate ascorbate to millimolar

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concentrations, with very high levels being recorded in those organs with an essential functional need for the 2-OGDDs, such as the adrenals and brain [11]. A variation in intracellular ascorbate could influence the activity of numerous 2-OGDDs and has been shown to affect the hypoxia-inducible factor (HIF) hydroxylases, affecting activation of the transcription factor HIF-1 [12–15] and HIF-1-dependent tumor growth in mice [16,17]. A lack of ascorbate inhibits HIF-1 hydroxylation and promotes HIF-1 activation [13,14], thereby potentially promoting tumor progression. Tumor ascorbate levels have rarely been measured, but we have shown that both endometrial and colorectal tumors contained relatively low levels of ascorbate, and this was associated with increased activation of the HIF-1 pathway [18,19]. Of particular interest was the observation that high-grade endometrial and colorectal tumors, with a highly dedifferentiated and aggressive phenotype, had significantly reduced capacity to accumulate ascorbate compared to surrounding normal tissue [18,19]. These results indicate that despite the same available plasma concentrations, these poorly vascularized tumors cannot acquire the same cellular ascorbate levels. Given the difficulty of some tumor regions in accessing the plasma supply, it is possible that better delivery of ascorbate to tumor cells may require supraphysiological plasma levels. To our knowledge, there are currently no data describing extravascular diffusion of ascorbate through tumor tissue and whether it is indeed likely to be limiting in hypoxic/avascular regions of a tumor. Obtaining diffusion data on ascorbate will be crucial both for understanding the need for optimal plasma levels as part of normal health maintenance and for the design of future cancer clinical intervention studies. Such information is increasingly needed to determine whether the widespread administration of ascorbate to cancer patients [20] is actually beneficial, and how. In this study, we have employed an in vitro pharmacokinetic model system that utilizes linear three-dimensional (3D) in vitro multicellular layers (MCLs) to represent the extravascular compartment and emulate tumor-like tissue. The MCLs are made by growing cells on a porous Teflon support membrane [21] to form diffusion-limited structures up to several hundred micrometers in thickness, with many features in common with spheroids [22], including central hypoxia and necrosis [23]. However, MCLs have a planar structure, making them particularly amenable to drug diffusion studies within a specialized diffusion chamber [24]. This in vitro model was initially developed to test the pharmacokinetics and pharmacodynamics of DNAand hypoxia-targeted anti-cancer compounds [25–27], some of which are currently undergoing clinical testing [28,29]. This model has been well-resolved to measure tissue penetration and cellular uptake, and we have now adapted this system to assess the availability of ascorbate throughout the extravascular compartment. Using this system, we have obtained data describing ascorbate diffusion and intracellular uptake and stability, which were then used to model ascorbate pharmacokinetics and diffusion through tissue. Pharmacokinetic simulations have revealed that ascorbate is heterogeneously distributed in normal and tumor tissues at physiological plasma levels, with severe penetration problems at suboptimal plasma concentrations. The data also provide insight into the range of plasma ascorbate concentrations and exposure times needed to saturate all regions of a tumor to fully support 2-OGDD activity.

Materials and methods Multicellular layers HT29 human colon adenocarcinoma cells (American Type Culture Collection) were maintained in monolayers in MEM-α medium

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(no nucleosides), 5% fetal bovine serum (FBS), penicillin (100 units/ml), and streptomycin (100 μg/ml) with weekly passaging (medium and supplements from Life Technologies, Gaithersburg, MD, USA). MCLs were grown on sterile collagen-coated Teflon support membranes in Millicell-CM inserts (Millipore Corp., Bedford, MA, USA) with a sterile polyethylene ring attached around the insert for flotation, as previously described [27]. HT29 cells were seeded at 1  106 cells per insert in 0.5-ml volume and floated in a large reservoir of medium (MEM-α with 10% FBS, 100 units/ml penicillin, and 100 μg/ ml streptomycin) for
6 h at 37 1C and 5% CO2 to allow cell adhesion. The inserts were then submerged in the medium using a stainless steel wide-mesh grid and incubated at 37 1C for 3 days in sealed, magnetically stirred jars.

Diffusion experiments The MCLs were inspected microscopically to verify uniform growth across the support. They were then inserted into the diffusion apparatus between two compartments (donor and receiver) of culture medium as previously described [27,30], containing 10 μM EDTA to prevent ascorbate oxidation with a final volume of 6.6 ml in each. The compartments were magnetically stirred in a 37 1C water bath and gassed with 95% N2 and 5% CO2 or 95% O2 and 5% CO2. Two radiolabeled internal standards, [14C]urea (Amersham Pharmacia Biotech, Piscataway, NJ, USA) and [3H]mannitol (ICN Pharmaceuticals, Waltham, MA, USA), were added together with fresh sodium L-ascorbate (Sigma–Aldrich) to the donor compartment. The flux of [14C]urea was used to determine the thickness of each MCL and [3H]mannitol flux was measured as marker of paracellular diffusion and MCL integrity [31]. A schematic of the diffusion chamber experimental setup is given in Fig. 1. Samples (100 μl) of both the donor and the receiver compartments were taken using a syringe over 5 h to monitor the flux through either the bare Teflon support (i.e., in the absence of cells) or the MCL. Samples were added to 100 μl of 0.54 M perchloric acid [containing 50 mM diethylenetriaminepentaacetic acid (DTPA)]. Of this, 50 μl was taken for scintillation counting in 3 ml scintillation fluid (Emulsifier Safe; PerkinElmer, Waltham, MA, USA) on a Packard Tri-Carb liquid scintillation counter. The remaining 150 μl was immediately frozen at 80 1C for ascorbate measurement by HPLC–ECD, using fresh sodium L-ascorbate standards (concentration verified by absorbance at 245 nm), as described previously [14].

Ascorbate stability, uptake, and turnover experiments in cell monolayers To constrain the model, parameters describing intracellular ascorbate uptake, stability, and turnover were obtained from HT29 cells in monolayer culture either under normoxic conditions or after equilibration at specified O2 levels in a Whitley H35 HypoxyStation (Don Whitley Scientific, Shipley, West Yorkshire, UK). Cells were incubated in ascorbate-free medium [Dulbecco's modified Eagle's medium (DMEM), 10% FBS, 100 units/ml penicillin, and 100 μg/ml streptomycin] for
16 h, then fresh sodium L-ascorbate was added to the culture medium to initiate the experiment. Over time the medium was sampled and cells were washed in phosphate-buffered saline, detached, and pelleted. Cell pellets and medium samples were extracted in 1:1 0.54 M perchloric acid (containing 50 mM DTPA) and H2O. Supernatants were then analyzed for ascorbate by HPLC–ECD as described [14], with cellular values normalized to cell number (by hemocytometer) and intracellular water volume of the derivative cell line WiDr, previously measured at 2.81 pl [14].

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Fig. 1. Schematic of diffusion experiments using multicellular layers (MCL). (A) HT29 MCL grown on a collagen-coated Teflon support. (B) Diffusion chamber where ascorbate and internal standards are added to the donor compartment to initiate the experiment with sampling from both compartments for 5 h. The Teflon support containing the MCL is located between the donor and the receiver compartments.

Data modeling and simulations Ascorbate transport in MCLs and tumors was modeled as previously described for chemotherapy drugs [25,30], using the Fick's Second Law equation for reaction–diffusion with explicit intracellular and extracellular compartments [28]. Ascorbate was assumed to diffuse via the paracellular route, and terms for instability and cellular uptake by active and passive transport were included (Eqs. (1) and (2)),   ∂C e ∂2 C e φ V max t C e V max e F ðO2 ÞC e ¼ DMCL 2  i þkt ðC e  C i Þ  ; ð1Þ ∂t φe K mt þ C e K me þ C e ∂x ∂C i V max t C e V C ¼ þ kt ðC e  C i Þ  max i i  kf F ðO2 ÞC i  kr C p ∂t K mt þ C e K mi þ C i

ð2Þ

where Ci and Ce are the intracellular and extracellular concentrations of ascorbate, Vmaxt and Kmt are the Michaelis-Menten parameters for active cellular uptake, kt is the passive transport, Vmaxe and Kme are the (oxygen-dependent) parameters for extracellular stability, Vmaxi and Kmi are parameters for intracellular degradation, kf and kr are the forward and reverse rate constants for intracellular equilibrium of ascorbate with other products (Cp), φi and φe (¼1 φi) are the intracellular and extracellular volume fractions in the MCL, and DMCL is the diffusion coefficient in the MCL. Oxygen dependence was introduced by allowing Vmaxe and kf to vary with oxygen concentration, being multiplied by a factor, FðO2 Þ ¼ ð1 þ ½O2 ÞN ;

ð3Þ

where N is a fitted parameter and [O2] is measured in %. Concentration–time data of [14C]urea, [3H]mannitol, and ascorbate flux through MCLs were fitted to a diffusion model (with initial conditions set to the initial measured concentration of compounds in the donor and receiver compartments) to obtain the MCL thickness (using the known diffusion coefficient of urea) or the diffusion coefficient through tissue (for mannitol and ascorbate). The flux experiments were performed on MCLs grown in ascorbate-containing medium (MEM-α is formulated with 50 μM ascorbate) and the cells already contained ascorbate. Therefore, the ascorbate data were fitted as simple diffusion. Parameters were fitted by nonlinear regression using a custom-written FORTRAN program as previously described [25,30] with the compound's diffusion coefficient in the support membrane fixed at the average value measured in separate stability experiments, where flux was measured through the bare support membrane only. Cell uptake data, obtained from HT29 monolayers, was modeled using the same equations with loss from

the medium described by Eq. (1) and the diffusion term set to 0 (no spatial gradient), with φi and φe replaced by the intracellular and extracellular volume fractions in the experiment. The model for cell uptake was fitted to the uptake data using Phoenix WinNonlin version 6.2 (Pharsight Corp.) with initial conditions set to the measured intracellular and extracellular ascorbate concentrations before and after introduction of exogenous ascorbate, respectively. One-dimensional simulations of tumor tissue penetration and cellular uptake were performed, in the same planar geometry as the MCL, using Mathematica version 9 (Wolfram Research) assuming cells were initially ascorbate deficient.

Virtual histology simulations in tumor and normal tissue Three-dimensional simulations were performed in a digitized microvascular network previously obtained from a mapped FaDu window chamber xenograft [32] to represent tumor tissue and a mapped rat cremaster muscle microvascular network [33] to represent well-organized normal tissue as previously described for anti-cancer prodrugs [34]. The 3D reaction diffusion equations are solved for oxygen and ascorbate using a Green's function approach [27,33], which calculates the oxygen and intracellular and extracellular ascorbate concentrations at each tissue point and includes extraction from the blood vessels. Two-dimensional “virtual histology” images of the oxygen and ascorbate distributions were produced in a representative tissue plane and distributions of concentrations calculated for the whole tissue region.

Results Diffusion of urea and mannitol Fig. 2 shows representative flux curves of urea, mannitol, and ascorbate through the bare support or through the MCL. The flux of [14C]urea (Fig. 2A and B) was used to calculate the thickness of each MCL, as well as being a marker of transport through the MCL and an internal standard for experiments measuring stability and bare support flux of ascorbate without MCLs present. The measured diffusion coefficient of urea through the bare support (Dsup; 1.77  10  6 70.04 cm2 s  1; n¼10) was identical to the historical average (1.77  10  6 70.03 cm2 s  1). The measured [14C]urea diffusion coefficient through MCLs (DMCL; 0.45  10  6 70.23 cm2 s  1; historical data) [35] was used to estimate the MCL thickness for

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Fig. 2. Flux of urea, mannitol, and ascorbate through a bare support or multicellular layer. Representative flux curves of (A, B) urea, (C, D) mannitol, and (E, F) ascorbate through the bare Teflon support membrane (A, C, E) and through a multicellular layer under anoxia (B, D, F). Raw data (symbols) and the fitted curves generated by the diffusion model (lines) are shown as the fractional concentration relative to the initial concentration in the donor compartment at time 0. The constant mass balance (average of the fractional concentration in the donor and receiver compartments) shows no loss of compound as it diffuses over the 5-h period, except for ascorbate, which was unstable at 95% O2(G). Diffusion is markedly slowed by the presence of the multicellular layer (B, D, F).

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each experiment, which ranged from 70.9 to 132.5 mm (n¼19), with Dsup fixed at 1.77  10  6 cm2 s  1. The diffusion of [3H]mannitol through each MCL was monitored as a marker of paracellular diffusion and MCL integrity (Fig. 2C and D). The measured Dsup, 1.14 70.04  10  6 cm2 s  1 (n ¼10) was used to fit the DMCL, and this was calculated as 0.256 70.06  10  6 cm2 s  1 (n¼ 19), in line with the historical average (0.217 0.1  10  6 cm2 s  1) [35]. Diffusion of mannitol through the bare support was slightly slower than that of urea because of its higher molecular weight (182 and 80 g mol  1, respectively). In addition, as mannitol can diffuse only paracellularly, its diffusion through the MCLs is also slower than that of urea, which is assumed to pass through cell membranes to a greater extent. The diffusion coefficient of ascorbate Four ascorbate concentrations were used to investigate ascorbate flux: 0.1 (n ¼ 2), 0.5 (n ¼ 10), 1 (n ¼5), and 10 mM (n ¼2). These concentrations represent the maximum plasma level achievable by dietary intake (0.1 mM) or bolus intravenous administration of
1 g (0.5 mM),
3 g (1 mM), or
50 g (10 mM) doses [36]. Ascorbate was stable in bare support flux experiments under anoxia (Fig. 2E and F) but unstable under highly oxic conditions (95% O2), with a half-life of
2 h in the medium (Fig. 2G). Therefore, all experiments were carried out under anoxia, which prevented ascorbate oxidation in the medium as seen by the constant mass balance in Fig. 2E and F.

The Dsup for ascorbate was estimated as 0.81 7 0.08  10  6 cm2 s  1 (n¼ 7), and DMCL as 0.213 70.11  10  6 cm2 s  1 (n ¼ 19). Ascorbate appeared to diffuse nonreactively (under anoxia) in MCL, slightly slower than mannitol, which has a very similar molecular weight (176 and 182 g mol  1, respectively), indicating that diffusion is predominantly via the paracellular route. The slightly lower DMCL of ascorbate compared to mannitol suggests that some cellular uptake or metabolism was occurring. The average, approximate intracellular ascorbate concentrations for whole MCLs were calculated assuming the same cell volume as WiDr cells (which are a derivative of HT29 cells [37]) of 2.81 pl [14] and were calculated at 0.15, 0.31, and 0.56 mM intracellular ascorbate for donor concentrations of 0.1, 1, and 10 mM, respectively, after 5 h. This indicates increased cellular uptake at higher concentrations, suggesting that cellular uptake could affect diffusion. Therefore, it was important to include cell transport parameters into the diffusion model next.

Constraining the model: ascorbate stability and transport parameters The ascorbate DMCL provides the basis of the diffusion model. However, to further define the model, parameters describing intracellular ascorbate uptake rates and stability were obtained in cells, as previously for drug uptake using this model [25]. Fig. 3 shows intracellular ascorbate uptake in HT29 cells in monolayer culture over 5 h at either 20 or 0.1% O2 with various initial extracellular concentrations. Normoxic conditions appeared to

Fig. 3. Intracellular ascorbate uptake in HT29 cell monolayers and oxygen-dependent ascorbate stability. HT29 cells were equilibrated at (A) normoxia or (B) 0.1% O2 and incubated for 5 h with increasing concentrations of fresh sodium L-ascorbate in the medium, and the intracellular ascorbate concentration was calculated. (C) Loss of intracellular ascorbate after removal of ascorbate in the medium under normoxia. (D) Oxygen-dependent instability of ascorbate in medium; fresh sodium L-ascorbate was added to full culture medium (DMEM þ10% FBS, no cells) and sampled over time under the specified oxygen tensions. Symbols show the ascorbate measurements and the lines show the cell uptake model fitted to all data simultaneously. From these data, Michaelis-Menten transport parameters and stability constants were fitted and added into the diffusion model for simulating transport and stability in tumors.

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slow down intracellular uptake compared to 0.1% O2 conditions (Fig. 3A and B). The rate of intracellular uptake increased with the available extracellular concentration, but was clearly capacity-limited as the uptake ratios fell markedly with concentration (Ci/Ce of 8.1, 1.4, and 0.3 for measured Ce of 0.1, 1, and 10 mM, respectively). This was not due to depletion in the medium as ascorbate was relatively stable under these conditions and total cellular uptake at 5 h accounted for only 2.3, 0.5, and 0.1% of the initial extracellular ascorbate at 0.1, 1, and 10 mM, respectively. Consequently these cell uptake data were modeled as capacity-limited transport (with Michaelis-Menten transport parameters). In addition to cellular transport kinetics, parameters describing ascorbate extracellular and intracellular stability were included in the model (Fig. 3; Table 1). In the absence of extracellular ascorbate, the intracellular half-life was
4 h under normoxia (Fig. 3C). In full culture medium (DMEM, 10% FBS), in the absence of cells, ascorbate decay was oxygen dependent, with a half-life of
5 h at 20% O2 and increasing stability at 5 and 1% O2 (Fig. 3D). The data were well fitted (Fig. 3) by a model that included active and passive cellular transport, oxygen-dependent extracellular instability, a low rate of oxygen-independent intracellular turnover, and an equilibrium with other products within the cell in which the forward rate constant was oxygen dependent (Eqs. (1)–(3) and Supplementary Fig. S1). Table 1 summarizes the fitted parameters included in the model and schematically represented in Supplementary Fig. S1. These parameters were used to simulate the penetration and cellular uptake of ascorbate in tumor tissue as a function of time and distance from the capillary using the tissue cell volume fraction of 0.517 for HT29 MCLs [38] and assuming that cells were initially ascorbate deficient. For the 1D simulations, a distance of 100 or 200 μm from the capillary (intervessel distance of 200 or 400 μm) was assumed. This models a situation intermediate between radial diffusion out of a central blood vessel (Krogh cylinder) and diffusion into a tumor cord from surrounding blood vessels. To include oxygen-dependent ascorbate instability, the oxygen distribution was modeled assuming a 50 μM (5% oxygen) concentration in the capillary, which leads to a gradient of oxygen in the tissue similar to that reported previously [39]. Two scenarios were simulated. One was of continuous ascorbate infusion for 24 h, which models steady state at either physiological plasma concentrations (10–100 μM, i.e., dietary intake) or pharmacological concentrations (1 or 10 mM, i.e., intravenous administration). The second scenario was an intravenous bolus dose of pharmacological concentrations, followed by plasma concentration decay

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with a half-life of 2 h, as previously determined by a human pharmacokinetic study [40]. Simulations of ascorbate diffusion through tumor tissue: physiological concentrations Fig. 4 summarizes the expected extracellular and intracellular ascorbate levels with deficient (10 μM), average (50 μM), or saturated (100 μM) physiological plasma concentrations at tissue depths of 100 and 200 μm. The simulations show that only at the 100 μM plasma concentration would intracellular ascorbate concentrations reach meaningful levels at 100-μm tissue depth. Furthermore, this took 16–24 h exposure to plateau. At average plasma ascorbate levels (50 μM), cells adjacent to the capillary were well supplied; however, ascorbate tissue penetration was severely impaired. At deficient plasma ascorbate levels (10 μM) there was very little intracellular accumulation, even in cells adjacent to the capillary. Simulations of ascorbate diffusion through tumor tissue: pharmacological concentrations Fig. 5A shows simulations of a pharmacological infusion achieving constant 1 mM plasma ascorbate levels. This scenario dramatically increased both tissue penetration and intracellular uptake, with little difference between the 100- and the 200-μm tissue depths, and intracellular concentrations reached over 1 mM. At the 10 mM constant plasma level, the whole tissue reached pharmacological concentrations, and intracellular ascorbate levels were maximal, reaching 10 mM at both tissue depths (Fig. 5B). The exposure time needed to reach intracellular plateau was
8 h, compared to 16–24 h needed at physiological plasma levels. Cells adjacent to the capillary showed slightly less intracellular uptake owing to the predicted relative oxic instability of ascorbate compared to 100- or 200-μm tissue depths. A common scenario is that of an intravenous bolus dose, which achieves pharmacological plasma concentrations of 1–10 mM, but with a half-life of 2 h [40]. Simulations of extracellular and intracellular ascorbate under these conditions are shown in Fig. 6. As with the constant infusion (Fig. 5), tissue penetration at these concentrations was considerable, with ascorbate able to diffuse to reach
50% of the plasma level at 200 μm. However, these peak plasma and tissue levels rapidly declined over
4 h. As cellular uptake does not reach a plateau until
8 h, intracellular levels were much lower compared to the infusion simulations (Fig. 5). However, most cells still accumulated 0.5–1 mM for up to

Table 1 Parameters obtained from HT29 MCL or monolayer experiments included in the model of ascorbate diffusion and cellular uptake in tumor tissue. Parameter

Description

Value

Units

SEa

SE%b

DMCL Vmaxt Kmt kt Vmaxe Kme kf kr Vmaxi Kmi N

Diffusion coefficient Vmax for cell transport Km for cell transport Passive cell transport rate constant Vmax for extracellular instability Km for extracellular instability Forward intracellular rate constantc Reverse intracellular rate constantc Vmax for intracellular turnover Km for intracellular turnover Parameter for oxygen dependence of ascorbate loss (Eq. (3))

0.213  10  6 0.0161 0.0102 0.0083 0.00092 7 0.00494 0.00718 0.0072 0.0514 0.785

cm2 s  1 mM min  1 mM min  1 mM min  1 mM min  1 min  1 mM min  1 mM mM

0.11 0.0003 0.0024 0.0004 0.00042 Fixed 0.00060 0.00091 0.0004 0.0088 0.167

5.0 1.9 23 4.4 46 — 12 13 6.1 17 13

a SE is the standard error of the parameter estimate calculated from 19 separate determinations of the parameter (for DMCL) or the asymptotic standard error calculated by the nonlinear regression routine in Phoenix WinNonlin version 6.2 when cell uptake parameters were fitted. b SE% is the SE as a percentage of the corresponding parameter value. c kf and kr are the forward and reverse rate constants for conversion of ascorbate to an intracellular product with which it is in equilibrium. kf and Vmaxe are assumed to be oxygen dependent (see Eqs. (1)–(3)).

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Fig. 4. Simulations of ascorbate tissue penetration and cellular uptake over time after a constant infusion at physiological levels. The ascorbate diffusion model was simulated using three physiological plasma ascorbate concentrations to predict the extracellular tissue levels (EC; left column) and the intracellular concentrations (IC; right column) achievable with each concentration at either 100- or 200-μm tissue depths or in cells adjacent to the capillary (IC 0 μm). The three concentrations represent (A) deficient, (B) average, or (C) saturated plasma levels.


8 h at the 1 mM bolus dose and much higher levels of 1–2.5 mM for up to
12 h at the 10 mM bolus dose.

avascular tissue reaching the physiological, millimolar range only at supraphysiological plasma levels of 4100 μM.

Simulations of ascorbate penetration and uptake at steady state

Virtual histology heat maps of ascorbate diffusion through tumor and normal tissue

Instead of ascorbate diffusion over time, diffusion as a function of distance from the capillary was also simulated, using five plasma ascorbate concentrations at steady state after 24 h of constant infusion (Fig. 7). These simulations predict concentration gradients throughout the tissue plane and show that ascorbate is likely to diffuse nonlinearly through tissue. At all physiological plasma ascorbate concentrations (10–100 μM), there was a significant gradient through tissue, with only proximal cells accumulating sufficient ascorbate. At pharmacological plasma concentrations there was no impediment to tissue penetration or cellular uptake. Taken together, these simulations support the hypothesis that at physiological plasma levels, ascorbate penetration to hypoxic tumor tissue is likely to be impaired, with intracellular levels in

Three-dimensional simulations were next performed to visualize the distribution of ascorbate through tumor tissue in two dimensions and to compare this with oxygen and also with normal tissue distribution. Mapped, digitized microvessel networks of FaDu xenografts from rat window chambers [32] or rat cremaster muscle tissue [33], previously used to simulate drug distribution [34], were used with the ascorbate diffusion model. The vascular network of normal tissue, which has a maximum intervessel distance of 50 μm, is clearly more organized and functional compared to the FaDu tumor tissue vasculature (Fig. 8) and is much better equipped to distribute both oxygen and ascorbate. At average physiological plasma ascorbate levels (50 mM), ascorbate appeared heterogeneously distributed, similar to oxygen. Oxygen has a

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Fig. 5. Simulations of ascorbate tissue penetration and cellular uptake over time after a constant infusion at pharmacological levels. The ascorbate diffusion model was simulated using two pharmacological plasma ascorbate concentrations, (A) 1 mM and (B) 10 mM, achievable with intravenous administration, to predict the extracellular tissue levels (EC; left column) and intracellular concentrations (IC; right column) at either 100- or 200-μm tissue depths or in cells adjacent to the capillary (IC 0 μm).

Fig. 6. Simulations of ascorbate tissue penetration and cellular uptake over time after bolus intravenous administration. The ascorbate diffusion model was simulated using two initial plasma ascorbate concentrations (1 and 10 mM) to predict the extracellular tissue levels (EC; left column) and intracellular concentrations (IC; right column) achievable with each dose at either 100- or 200-mm tissue depths or in cells adjacent to the capillary (IC 0 μm). (A) 1 mM plasma ascorbate achievable with
1 g intravenous dose. (B) 10 mM plasma ascorbate achievable with
50 g intravenous dose.

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Fig. 7. Simulated concentration gradient of ascorbate in tumor tissue at steady state after 24 h constant infusion. Modeled extracellular and intracellular ascorbate concentrations are shown according to tissue depth/distance from capillary. Physiological plasma ascorbate levels (below 100 μM) may result in impaired tissue penetration and low intracellular concentrations. This is markedly improved at concentrations 4100 μM.

high tissue diffusion coefficient (13.5  10  6 cm2 s  1), but its rapid metabolism prevents further penetration. In comparison, ascorbate has a relatively low diffusion coefficient (0.21370.11  10  6 cm2 s  1), with moderate oxygen-dependent instability in tissue. This indicates

that ascorbate is well suited to supplying cells near to blood vessels, whereas remote and hypoxic tumor cells are not likely to be able to access sufficient concentrations required for millimolar uptake. These simulations are in good agreement with the 1D simulations (Figs. 4–7),

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Fig. 8. Virtual histology heat maps of extracellular and intracellular ascorbate in tumor and normal tissue compared to oxygen. Microvessel networks of (A) FaDu xenograft tissue in rat window chamber or (B) normal rat cremaster muscle are shown. Images show tissue regions that range from ascorbate or oxygen deficient (blue) to saturated (red). Lines depict blood vessels, with normal tissue having an organized network as opposed to the irregular pattern in tumor tissue. Images are from (A) the 75-μm into the 150-μm z-plane for the tumor network and (B) the 120-μm into the 240-μm z-plane of the cremaster muscle region. Note that the cremaster network is not cuboidal and blue areas outside the network are not included. The entire blood vessel network is superimposed and blood vessels are scaled to 25% of normal size for clarity. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

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Table 2 Summary of average ascorbate concentrations in tumor and normal tissue simulations. Simulated parameter

Predicted ascorbate or O2 concentration (μM) Mean

SD

Tumor tissue 50 μM plasma ascorbate Tumor O2a Tumor EC ascorbate Tumor IC ascorbate Total ascorbate

9.98 16.9 293 155

8.92 8.62 157 111

0.00 0.04 0.19

46.4 48.2 696

100 μM plasma ascorbate Tumor O2a Tumor EC ascorbate Tumor IC ascorbate Total ascorbate

9.98 60.5 722 391

8.92 12.9 120 85.1

0.00 2.97 3.45

46.4 96.2 899

500 μM plasma ascorbate Tumor O2a 9.98 Tumor EC ascorbate 464 Tumor IC ascorbate 1500 Total ascorbate 982

8.92 14.4 22.4 18.9

0.00 136 1100

46.4 499 1540

Normal tissue 50 μM plasma ascorbate Normal O2a Normal EC Normal IC Total ascorbate

22.0 32.3 532 282

9.23 5.87 77.9 55.2

2.32 17.8 293

48.8 49.7 708

100 μM plasma ascorbate Normal O2a Normal EC Normal IC Total ascorbate

22.0 82.6 856 469

9.23 5.80 21.4 15.7

2.32 68.1 791

48.8 99.8 914

9.23 5.66 2.99 4.53

2.32 469 1470

48.8 500 1500

500 μM plasma ascorbate Normal O2a 22.1 Normal EC 483 Normal IC 1480 Total ascorbate 981

Min

Max

Total ascorbate ratio (tumor/normal) 50 μM 54.9% 100 μM 83.3% 500 μM 100% Three ascorbate concentrations representing average (50 μM), saturated (100 μM), and supraphysiological (500 μM) plasma levels are summarized and compared to a constant oxygen level (50 μM; 5%). The predicted tissue concentrations in normal or tumor tissue are compared. a Oxygen concentration in blood supply is simulated at a constant level of 50 μM (5%).

in which plasma ascorbate concentrations 4100 μM are necessary for full distribution in tumor tissue. Although the maximum intervessel distance is only 200 μm in the FaDu tumor network, it also includes extraction of ascorbate from the capillaries. Despite higher oxygen concentrations in the normal tissue simulations, ascorbate is more homogeneously distributed even at low plasma concentrations (Fig. 8B) as a result of lower intervessel distances and a more efficient and uniform microvascular network. Table 2 summarizes the expected ascorbate concentrations in tumor compared to normal tissue as simulated by the model. The average calculated ratio of total ascorbate in tumor:normal tissue (54.9–83.3% at physiological plasma levels; Table 2) was similar to that seen in high-grade colorectal and endometrial tumors (61 and 67%, respectively [18,19]).

Discussion The results presented here are, to our knowledge, the first data to describe ascorbate tissue diffusion. Utilizing a highly relevant in vitro

pharmacokinetic model employing MCLs, we have obtained the diffusion coefficient of ascorbate through tissue, which in combination with uptake and stability data, has enabled the simulation of ascorbate penetration and cellular uptake. The simulations suggest that at physiological plasma levels (o100 μM), cellular uptake at distances of greater than 100 μm from the vascular supply is likely to be impaired because of insufficient penetration and that the availability of ascorbate is highly dependent on plasma supply. Intracellular ascorbate concentrations are maintained by the SVCTs [1] and most cells concentrate ascorbate to 0.5–10 mM [11,41], which is also the optimal concentration range to maintain 2-OGDD activity (
1–3 mM) [42,43]. An optimal plasma level to achieve tissue saturation is
80 μM in healthy adults, which corresponds to a dietary intake of
200 mg per day. These data fit closely to our model, in which a constant, high physiological ascorbate concentration of 100 μM would provide intracellular levels of 0.5–1 mM at up to 100 μm tissue depth. This plasma level can be achieved through dietary means alone. According to our model, concentrations of 50 μM, which reflect “healthy” but not saturated plasma ascorbate levels [5], could result in compromised availability within the normal intervessel distance of 50 μm. In support of this prediction, it has been reported that cellular uptake is significantly impaired if plasma levels fall below
20 μM [5]. Our study is also highly relevant to cancer patients, as their plasma ascorbate levels are known to be lower than those of healthy controls. Studies have shown mean plasma levels of 15 μM in lung cancer patients, compared to 47 μM in healthy controls [44], and a mean plasma concentration of 18 μM in patients with oral squamous cell carcinoma compared to 57 μM in healthy controls [45]. We have predicted here that plasma levels of 10 μM, which may be quite common in cancer patients [46], would result in drastically impaired tumor tissue penetration, and even the most proximal cells will not be able to accumulate sufficient ascorbate. This has implications not only for tumor biology, but also for the overall health status of the individual, as 2-OGDD activity may be compromised globally. In addition to low plasma ascorbate levels, poor vascularization of solid tumors is likely to be a further barrier to tissue ascorbate availability, and our data indicate that constant, supraphysiological plasma levels (4100 μM) could overcome this. The common scenario of bolus intravenous administration can increase plasma levels to 1–10 mM [36], and this could maximize tissue penetration beyond 100 μm (intervessel distances 4200 μm). It could also bolster intracellular levels above 1 mM, which may further dampen an active HIF-1 response and/or optimize activity of other 2-OGDDs [14]. Our simulations suggest that, if optimal intracellular ascorbate concentrations are to be achieved in all cells within a tumor, multigram intravenous infusion may increase distant tissue levels enough to adequately increase cellular uptake. Bolus intravenous administration resulting in plasma levels of 1–10 mM overcomes the tissue penetration issue, although the short half-life of ascorbate at these levels means that, particularly with 1 mM concentration, distant cells will not exceed intracellular levels of 0.5–1 mM. Therefore, if a bolus dose is to be used, 10–50 g may be a more effective dose, providing peak plasma levels of
6–13 mM for 2–4 h [36], which is sufficient for cell uptake 41 mM. However, if a longer infusion were given for
2 h, much lower doses of only 1–3 g could be used to give plasma concentrations of 1–2 mM [36], which may be sufficient for tissue penetration and cellular uptake. Our model and simulations predicted that tumor tissue would contain 55–83% of the normal tissue ascorbate level at physiological plasma concentrations. Interestingly, we have previously measured a very similar ratio in human tumor and matched normal tissue in high-grade endometrial and colorectal tumor tissue [18,19]: the median tumor:normal ascorbate ratio was 67% and 61%, respectively. In contrast, in low-grade tumors, which are more likely to be well vascularized, this ratio was closer to 100%

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[18,19]. This indicates that our model has good clinical relevance to poorly vascularized tumor tissue. In addition, our previous studies showed that low tumor ascorbate content was associated with shorter disease-free survival in colorectal cancer patients, which suggests that ascorbate may inhibit tumor progression [18]. Based on current and emerging knowledge, ascorbate could contribute to a number of anti-cancer mechanisms, including the regulation of HIF-1 [12,14] and the regulation of other 2-OGDDs with epigenetic effects [47]. Recent studies have demonstrated significant ascorbate dependence of the Ten–Eleven Translocation enzymes, also members of the 2-OGDD family, which hydroxylate 5-methylcytosine leading to demethylation and changes in gene expression [48–50]. This may also be a clinically relevant activity of ascorbate. Our simulations suggest that intravenous ascorbate administration could produce pharmacological levels of ascorbate in tumor tissue (
5 mM after a bolus dose), which may also be sufficient to result in a significant pro-oxidant effect via generation of H2O2, and this may be cytotoxic to tumor cells [51]. Our model predicts that this could be maintained for a period of several hours after the infusion, but whether this mechanism occurs in vivo remains to be shown. The data suggest that ascorbate diffuses nonlinearly through tissue and may follow a pattern similar to that of oxygen [52]. Therefore, it is possible that the associations between low ascorbate and high HIF-1 activation and poor disease-free survival in clinical samples [18,19] reflect tissue oxygenation status, rather than affecting 2-OGDD activity. However, HIF-1 is known to be activated under a variety of nonhypoxic conditions, such as metabolic disturbance [53], and the clinical associations we observed [18] were independent of tumor grade and stage. That hypoxia is likely to be coincident with ascorbate deficiency may serve to further inhibit activity of susceptible 2-OGDDs and amplify HIF activation. Therefore, increasing ascorbate availability to tumor tissue may help restore a more normalized cellular response to hypoxia. The data modeling performed here is limited by the strength of the incorporated parameters. To further strengthen the model, future studies will need to specifically define the oxidation rate of ascorbate to dehydroascorbate (DHA). Although DHA accounts for only
5% of total ascorbate in biological fluids and is rapidly reduced back to ascorbate intracellularly [54], this may become an important reservoir in highly oxidizing microenvironments. However, whether DHA levels increase significantly in tumors is difficult to determine. In addition, plasma ascorbate levels are likely to peak and trough after dietary intake, and this could also influence the model. The baseline intracellular ascorbate concentrations may also influence diffusion, as deficient cells will sequester ascorbate and reduce penetration to distal cells. The Km for ascorbate uptake modeled here (10.2 μM) is in the lower range of previous calculations for SVCT2 of 8–62 μM in various other cell lines [6], and as such, estimates of intracellular uptake represent conservative examples. Further studies are required to clarify whether ascorbate plays a direct role in regulating 2-OGDDs and which enzymes are most susceptible to ascorbate loss. More pressing perhaps, is the need for thorough clinical intervention data to determine whether these effects of ascorbate are powerful enough to improve clinical outcomes. Pharmacokinetic data such as we have described here provide a useful tool to guide the use of ascorbate to ensure optimal tissue delivery and will be crucial in the design of future intervention studies.

Acknowledgments We thank Drs. Anitra Carr and Gabi Dachs for their critical review of the manuscript. C. Kuiper was supported by a Bright

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Future Top Achiever Doctoral Scholarship by the Tertiary Education Commission, New Zealand.

Appendix A. Supporting information Supplementary data associated with this article can be found in the online version at http://dx.doi.org/10.1016/j.freeradbiomed. 2014.09.023.

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